Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 22. #16840165 | C4 | semidirect |
| 23. #16840165 | C4 | semidirect |
| 26. #16840160 | C4 | semidirect |
| 30. C61×#498 | C4 | semidirect |
| 188. #498 | #6923 | semidirect |
| 204. C61 | #9749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#6923 | 2 |
| #21461367 | 2 |
| #21461203 | 2 |
| #21461202 | 2 |
| #21461129 | 2 |
| #21461128 | 2 |
| #21456328 | 2 |
| #9749 | 61 |